4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either be N or B?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
![4. How many permutations are there of the letters in the word BALLOON if the first and the last letters must either
be N or B?
5. In how many ways can you seat two children and three adults in a row of five seats if the children are not to sit
together?
6. Find in how many ways can two admirals, three generals, and four lieutenants can be seated in a row of nine seats
of (a) the admirals sit at each end. (b) a general sit at each end and the lieutenants in consecutive seats.
7. A baseball tgam has 16 players. Suppose that the team has three star players: Ryan, Glenn and Manny, and that
they must be first, second and third, respectively. How many different batting orders are there for the team?
8. Seven boys and seven girls went to watch a movie. How many ways can they be seated if (a) the boys are to sit
together and so with the girls? (b) the boys and the girls are to sit alternately? (c) Grace and Joey are members of
the group and want to sit together all the time?
9. In how many ways can you sit 8 people on a round table (a) if there are no restrictions? (b) if two particular persons
want to sit next to each other?
10. Crisha has 5 different colored beads including purple and pink. In how many ways can she arrange the beads in a
string (a) if there are no restrictions? (b) so that the purple and pink beads are adjacent to each other?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F938584e8-8fa7-452b-93ba-60a67832a84e%2F97cdd14c-2f4b-46c1-8131-827a7359b57d%2F3y0g41r_processed.jpeg&w=3840&q=75)
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